Two complementary approaches are necessary to understand galaxy evolution: on the one hand, we need to develop theoretical models for galaxy formation, chemical and dynamical evolution, and on the other hand, we need to collect as many and as accurate as possible observational data to constrain such models. In particular, we need to know the masses, chemical abundances and kinematics of the various galactic components, namely gas, stars and dark matter; we need to know the star formation history (SFH), the initial mass function (IMF), etc. In this review our current knowledge of the SFHs, as derived from the colour-magnitude diagrams (CMDs) of their resolved stellar populations, is summarized.
Resolved stellar populations are the best tracers of the SFH of a galactic region, and their CMD the best tool to exploit the tracers. This is due to the well known circumstance that the location of any individual star in a CMD is uniquely related to its mass, age and chemical composition. From the CMD we can thus disentangle directly these evolution parameters. In the case of simple stellar populations, i.e. coeval stars with the same chemical composition, isochrone fitting is the most frequently used method to infer the system age. In the case of galaxies, with rather complicated mixtures of different stellar generations, the age determination is less straightforward, but their CMDs remain the best means to derive the SFH.